Assortment Planning and Inventory Decisions Under Stockout-Based Substitution

Given a finite set of products with varying prices and costs, stochastic demand and customer preferences, we consider the problem of determining the optimal assortment and inventory levels in order to maximize expected profit in a single-period. We model customer preferences through the definition of customer types, where a type is a ranking of the potential products by order of preference. A customer purchases the highest ranked product available (if any) in the assortment at the time of his visit to the store (dynamic substitution). The total demand comprises of a fixed proportion of customers of each type. We show that an efficient dynamic programming algorithm of pseudo-polynomial complexity O(8) can be used to determine the optimal assortment. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known heuristics, especially when the average demand is high and customers have large sets of preferred products.